The victory was Atlanta's seventh in eight games and moved the Braves to six games behind the Nationals in the National League East after Washington lost to San Francisco. Atlanta remained one game behind the Giants for the second NL Wild Card spot.
With Atlanta leading, 1-0, in the eighth, Minor walked Zack Cozart with one out, issuing his fourth free pass of the game. Pinch-hitter Chris Heisey followed with a slow ground ball to third that Chris Johnson scooped and threw to first for the second out, but Cozart moved to second and scored on Hamilton's flare up the middle.
Hamilton was Minor's last hitter of the night, but the 26-year-old left-hander became the first opposing pitcher to take a no-hitter into the eighth inning at Great American Ball Park.
"I'd say it was probably the fourth inning when I noticed no hits up there," Minor said. "But my main concern was the 1-0 game; that's what contributed to the walks -- kind of pitching around guys … because I feel like we need to win every game right now."
Minor gave way to reliever Jordan Walden, who ended the inning on a groundout by Todd Frazier that Johnson made a diving play on to prevent the go-ahead run from scoring.
After having a scheduled start skipped earlier this month, Minor has been sensational. In three outings since then, he's posted a 2.53 ERA. In his 10 prior starts, he had a 7.33 ERA. His decline came after a breakout season in 2013 in which he posted a career-best 3.21 ERA and a start to the 2014 campaign that included a 3.07 ERA through his first seven outings.
Minor credited a change in mindset for his recent turnaround, as well as some help from rotation mate Ervin Santana, whom he solicited for tips on how to grip the ball on certain pitches. He practiced using the new grips while throwing bullpen sessions following his skipped start, and they've produced more movement on his two-seam fastball and his slider.
Minor's adjustment to the mental side of his game was aided by a talk he had with manager Fredi Gonzalez and pitching coach Roger McDowell.
"It was kind of, 'Let's start fresh right here and finish the season strong,'" Minor said of that conversation.
"I kind of threw away everything and kind of went out there like my old self last year. I don't think about my previous starts -- I think that's what I was doing earlier in the year. I was kind of leaning on those starts and hoping I didn't repeat that, and kept on going all year, one bad start after the other."
Minor's outing Friday was his longest since July 21, 2013, against the White Sox, when he went eight innings. He allowed one hit in a start for the first time since Sept. 5, 2012, against the Rockies.
"His command was outstanding and he had stuff that was electric," Gonzalez said. "He's carrying that momentum, and you can see the confidence building by every start, every pitch."
The player responsible for ensuring that Minor's brilliant effort didn't go to waste is on quite a tear at the plate. Upton's home run was his 25th of the season, and he went 3-for-6 with a triple to extend his hitting streak to 13 games. He's batting .413 with five homers and 20 RBIs over that span.
"[Manny Parra] made a very good pitch on me the first pitch -- a fastball down," Upton said of his 12th-inning at-bat. "The next pitch was an offspeed pitch up in the zone that stayed up for me."
Atlanta's only scoring before the 12th came on a Tommy La Stella fielder's choice ground ball with the bases loaded in the second, scoring Freddie Freeman to make it 1-0.
Atlanta's bullpen was excellent after Minor left the game, tossing 4 1/3 scoreless frames. Reliever David Hale came on in the 11th and escaped a two-on, one-out jam to preserve the tie. Hale also earned the win.
Craig Kimbrel came on in the bottom of the 12th and picked up his 38th save, tying him with Milwaukee's Francisco Rodriguez for the NL lead.
Atlanta managed to win despite going 1-for-8 with runners in scoring position and leaving 13 runners on base.
But the Braves will take the win.
"We fought," Upton said. "We weathered two innings from [Reds closer Aroldis Chapman] and the back end of their bullpen, and we put ourselves in a position to win, and we finally got it done."
Getting it done is what matters as September approaches, and Atlanta is in the thick of a pennant race. With an offense that has seen a recent rejuvenation to go along with the rejuvenation of a key piece in their rotation in Minor, the Braves are excited for what lies ahead over the final five weeks of the regular season.
"It's great. It's a time that you need it," Minor said of how the Braves persevered on Friday. "Early in the year, you need those games, but it always comes down to the end where everybody's scratching and clawing to try and get those wins.
"And we're all clicking right now -- offense, defense, you name it. So it's coming at a good time."